Feedback in the Non-Asymptotic Regime

Abstract

Abstract-Without feedback, the backoff from capacity due to non-asymptotic blocklength can be quite substantial for blocklengths and error probabilities of interest in many practical applications. In this paper, novel achievability bounds are used to demonstrate that in the non-asymptotic regime, the maximal achievable rate improves dramatically thanks to variable-length coding and feedback. For example, for the binary symmetric channel with capacity 1=2 the blocklength required to achieve 90% of the capacity is smaller than 200, compared to at least 3100 for the best fixed-blocklength code (even with noiseless feedback). Virtually all the advantages of noiseless feedback are shown to be achievable, even if the feedback link is used only to send a single signal informing the encoder to terminate the transmission (stop-feedback). It is demonstrated that the non-asymptotic behavior of the fundamental limit depends crucially on the particular model chosen for the "end-of-packet" control signal. Fixed-blocklength codes and related questions concerning communicating with a guaranteed delay are discussed, in which situation feedback is demonstrated to be almost useless even non-asymptotically.

Short-blocklength non-binary LDPC codes with feedback-dependent incremental transmissions

“…The reason for selecting a higher-rate code for k = 96 is given in Sec. V and a complete description of the non-binary codes used in this paper is available online 1 .…”

“…5: Empirical probability of additional incremental bits required to decode correctly in the VLFT setting for k=96 bits and initial blocklengths of 120 and 128 bits corresponding to rate-0.8 and rate-0.75 non-binary LDPC codes respectively [1], and throughput for transmission without feedback [4] with a decoding error probability of 10 −6 . The simulation points follow R t = k λ .…”

“…Polyanskiy et al [1] and Chen et al [2] illustrated that by using feedback, one can approach capacity in a small number of channel uses (low latency). Polyanskiy et al [1] introduced variable-length coding with termination (VLFT) which theoretically approaches capacity at low latencies.…”

“…Polyanskiy et al [1] introduced variable-length coding with termination (VLFT) which theoretically approaches capacity at low latencies. In VLFT, the receiver provides full noiseless feedback to the transmitter.…”

“…Polyanskiy et al [4] illustrated that in a non-feedback communication system, the maximum achievable throughput is significantly lower for short blocklengths of up to several hundred bits. They later showed [1] that with feedback the maximum achievable throughput can be greatly improved at short blocklengths. They also concluded that variable-length coding in conjunction with feedback theoretically results in This material is based upon work supported by the National Science Foundation under Grant Numbers 1162501 and 1161822.…”